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Dynamical systems theory applied to short walking trials.

Sandesh G Bhat1, Kenton R Kaufman1

  • 1Motion Analysis Laboratory, Mayo Clinic, 565 1(st) St SW, DA 4-214, Rochester, MN 55905, USA.

Journal of Biomechanics
|September 28, 2024
PubMed
Summary

Analyzing human gait dynamics, this study compared methods for calculating stability and chaos. Semi-analytical techniques, particularly Method C, provided the most accurate gait analysis for older adults.

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Area of Science:

  • Biomechanics
  • Dynamical Systems Theory
  • Neuroscience

Background:

  • Human walking is a complex neuromuscular activity challenging to quantify.
  • Dynamical systems theory offers tools like Floquet multipliers (FM) and Lyapunov exponents (LE) to analyze gait stability and chaos.
  • Existing methods for calculating FM and LE vary, impacting results.

Purpose of the Study:

  • To compare three distinct methods (A, B, C) for calculating FM and LE in human gait.
  • To evaluate the accuracy of these methods in analyzing gait dynamics in older adults.
  • To establish a methodological foundation for gait analysis using short time-series data.

Main Methods:

  • Method A: False nearest neighbors and numerical approximation.
  • Method B: False nearest neighbors and semi-analytical technique.
Keywords:
Dynamical systemsFall riskGait analysisGait dynamicsStability

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  • Method C: Singular value decomposition and semi-analytical technique.
  • Analysis of surrogate center of mass trajectory in the transverse plane for 33 healthy older adults.

    • Main Results:

    • Semi-analytical methods (B and C) approximated observed gait behavior more closely than numerical methods.
    • Method C's LE and FM values most accurately matched subjects' gait patterns.
    • Discrepancies were found in LE and FM calculations across methods, affecting chaos and stability classifications.

    Conclusions:

    • Methodological choices significantly influence the assessment of gait stability and chaos.
    • Semi-analytical techniques, especially Method C, are recommended for accurate gait dynamics analysis.
    • This study provides a foundation for understanding gait stability and chaos using short time-series data.